America bought the Louisiana Purchase from France. France never had any meaningful presence in that territory; being incapable of defending the territory should America decide to take it anyway is probably a big part of the reason they decided to accept money for it.

Now my question: having purchased that land from France, did America have a right to eject the native people who lived there? Or did France in fact have no right to sell that land which, in all practical ways, actually belonged to the people who lived there?

Israel "bought" that land from people who had no legitimate ownership of the land in the first place.

That was a very different situation. That area had been under ottoman rule for generations. There was a long history of ownership.

The Ottomans had no legitimate right to sell that land out from under the people who actually lived there. The whole premise of Zionism is just one of many cases of European colonialism, and no more legitimate than any of the rest.

Why did the owners (under Ottoman law) not have the right to sell? How is/was that different from any property sale at the time, or now?

It wasn't their land, the Ottomans were just another imperial power.

(I know I'm talking to a wall here, getting you people to think outside of a legalistic mindset is impossible.)

I'm not trying to be specifically legalistic, just trying to see if there is some general principles here that you think apply outside this situation.

You see the rule of the ottomans as invalid, and this all (legalistic) property rights during that period invalid? That seems it would apply everywhere. How are property rights ever established? What does it take to invalidate them?